Weak Equivalence of Stationary Actions and the Entropy Realization Problem
نویسنده
چکیده
We initiate the study of weak containment and weak equivalence for μ-stationary actions for a given countable group G endowed with a generating probability measure μ. We show that Furstenberg entropy is a stable weak equivalence invariant, and furthermore is a continuous affine map on the space of stable weak equivalence classes. We prove the same for the associated stationary random subgroup (SRS). Applying these results to the entropy realization problem for ergodic stationary actions, we show that the set of values of the Furstenberg entropy of boundary actions is closed. This is obtained as an application of the omitting types theorem in first-order logic for metric structures.
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